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If the velocity of an object is decreasing at a constant rate, does it mean that it's a uniformly accelerated motion?

Physics Asked by khan Abdullah on July 4, 2021

If the velocity is constantly decreasing from $u$ to $v$ so is it uniformly accelerated motion?

One Answer

The acceleration is defined as begin{equation} frac{dvec{v}}{dt} = vec{a} end{equation}
I you mean with "decreasing" that $v = |vec{v}|$ decreases at a constant rate, then $a = |vec{a}| = a_0$ and the integration of the first equation leads to begin{equation} v(t) = -a_0t + v_0 end{equation}
with $a_0 > 0$ and $v_0$ some initial velocity.
From this it is easy to see that for fixed time intervals $Delta t = t_2 - t_1$ the change of velocity $Delta v$ is always the same regardless of $t_1, t_2$ as long as $Delta t$ remains fixed. The motion is indeed uniform acceleration.
However, the acceleration takes into account how the velocity-vector changes. Hence changing direction is also due to an acceleration. Take the uniform circular motion, the length of the vector $vec{v}$ stays everywhere the same but there is an acceleration due to the constant changing of the direction of this vector. This is also uniform acceleration as the the direction of $vec{a}$ changes, but its length remains fixed.

Answered by JulianDeV on July 4, 2021

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